decide whether each limit exists. if a limit exists, estimate its value. (a) $lim_{x\rightarrow1}g(x)$ (b)…
decide whether each limit exists. if a limit exists, estimate its value. (a) $lim_{x\rightarrow1}g(x)$ (b) $lim_{x\rightarrow2}g(x)$ (a) what is the value of the limit? select the correct choice below and, if necessary, fill in the answer box within your selection. a. $lim_{x\rightarrow1}g(x)=square$ b. the limit does not exist.
Answer
Explanation:
Step1: Analyze left - hand limit as x→1
As x approaches 1 from the left, g(x) approaches 2.
Step2: Analyze right - hand limit as x→1
As x approaches 1 from the right, g(x) approaches 2. Since the left - hand limit and the right - hand limit are equal as x→1, the limit exists.
Step3: Analyze left - hand limit as x→2
As x approaches 2 from the left, g(x) approaches 3.
Step4: Analyze right - hand limit as x→2
As x approaches 2 from the right, g(x) approaches 1. Since the left - hand limit and the right - hand limit are not equal as x→2, the limit does not exist.
Answer:
(a) A. $\lim_{x\rightarrow1}g(x)=2$ (b) B. The limit does not exist.